Enabling ultrastrong-coupling phenomena with single-drive Jaynes--Cummings models

We propose the effective simulation of light-matter ultrastrong-coupling phenomena with strong-coupling systems. Recent theory and experiments have shown that the single-atom quantum Rabi model can be simulated by the Jaynes-Cummings model with two additional classical drives. Here, we show that quantum nonlinear optical phenomena, relying on the counter-rotating terms of the quantum Rabi model, can be implemented by the Jaynes-Cummings and Tavis-Cummings models with only a single classical drive. We analyze three examples (one atom exciting two photons, frequency conversion, and one photon exciting two atoms) and show that they could be demonstrated with several currently available experimental quantum-optics systems, including superconducting circuits and trapped ions.